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/* mpfr_atan2 -- arc-tan 2 of a floating-point number
Copyright 2005 Free Software Foundation.
This file is part of the MPFR Library, and was contributed by Mathieu Dutour.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin Place, Fifth Floor, Boston,
MA 02110-1301, USA. */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
int
mpfr_atan2 (mpfr_ptr dest, mpfr_srcptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
mpfr_t tmp, pi;
int inexact;
mp_prec_t prec;
mp_exp_t e;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
MPFR_LOG_FUNC (("y[%#R]=%R x[%#R]=%R rnd=%d", y, y, x, x, rnd_mode),
("atan[%#R]=%R inexact=%d", dest, dest, inexact));
/* Special cases */
if (MPFR_ARE_SINGULAR (x, y))
{
/* atan2(0, 0) does not raise the "invalid" floating-point
exception, nor does atan2(y, 0) raise the "divide-by-zero"
floating-point exception.
-- atan2(0, -0) returns pi.313)
-- atan2(0, +0) returns 0.
-- atan2(0, x) returns pi, for x < 0.
-- atan2(0, x) returns 0, for x > 0.
-- atan2(y, 0) returns -pi/2 for y < 0.
-- atan2(y, 0) returns pi/2 for y > 0.
-- atan2(oo, -oo) returns 3pi/4.
-- atan2(oo, +oo) returns pi/4.
-- atan2(oo, x) returns pi/2, for finite x.
-- atan2(y, -oo) returns pi, for finite y > 0.
-- atan2(y, +oo) returns 0, for finite y > 0.
*/
if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y))
{
MPFR_SET_NAN (dest);
MPFR_RET_NAN;
}
if (MPFR_IS_ZERO (y))
{
if (MPFR_IS_NEG (x)) /* +/- PI */
{
set_pi:
if (MPFR_IS_NEG (y))
{
inexact = mpfr_const_pi (dest, MPFR_INVERT_RND (rnd_mode));
MPFR_CHANGE_SIGN (dest);
return -inexact;
}
else
return mpfr_const_pi (dest, rnd_mode);
}
else /* +/- 0 */
{
set_zero:
MPFR_SET_ZERO (dest);
MPFR_SET_SAME_SIGN (dest, y);
return 0;
}
}
if (MPFR_IS_ZERO (x))
{
set_pi_2:
if (MPFR_IS_NEG (y)) /* -PI/2 */
{
inexact = mpfr_const_pi (dest, MPFR_INVERT_RND(rnd_mode));
MPFR_CHANGE_SIGN (dest);
mpfr_div_2ui (dest, dest, 1, rnd_mode);
return -inexact;
}
else /* PI/2 */
{
inexact = mpfr_const_pi (dest, rnd_mode);
mpfr_div_2ui (dest, dest, 1, rnd_mode);
return inexact;
}
}
if (MPFR_IS_INF (y))
{
if (!MPFR_IS_INF (x)) /* +/- PI/2 */
goto set_pi_2;
else if (MPFR_IS_POS (x)) /* +/- PI/4 */
{
if (MPFR_IS_NEG (y))
{
rnd_mode = MPFR_INVERT_RND (rnd_mode);
inexact = mpfr_const_pi (dest, rnd_mode);
MPFR_CHANGE_SIGN (dest);
mpfr_div_2ui (dest, dest, 2, rnd_mode);
return -inexact;
}
else
{
inexact = mpfr_const_pi (dest, rnd_mode);
mpfr_div_2ui (dest, dest, 2, rnd_mode);
return inexact;
}
}
else /* +/- 3*PI/4: Ugly since we have to round properly */
{
mpfr_t tmp;
MPFR_ZIV_DECL (loop);
mp_prec_t prec = MPFR_PREC (dest) + BITS_PER_MP_LIMB;
mpfr_init2 (tmp, prec);
MPFR_ZIV_INIT (loop, prec);
for (;;)
{
mpfr_const_pi (tmp, GMP_RNDN);
mpfr_mul_ui (tmp, tmp, 3, GMP_RNDN); /* Error <= 2 */
mpfr_div_2ui (tmp, tmp, 2, GMP_RNDN);
if (mpfr_round_p (MPFR_MANT (tmp), MPFR_LIMB_SIZE (tmp),
MPFR_PREC (tmp)-2,
MPFR_PREC (dest) + (rnd_mode == GMP_RNDN)))
break;
MPFR_ZIV_NEXT (loop, prec);
mpfr_set_prec (tmp, prec);
}
MPFR_ZIV_FREE (loop);
if (MPFR_IS_NEG (y))
MPFR_CHANGE_SIGN (tmp);
inexact = mpfr_set (dest, tmp, rnd_mode);
mpfr_clear (tmp);
return inexact;
}
}
MPFR_ASSERTD (MPFR_IS_INF (x));
if (MPFR_IS_NEG (x))
goto set_pi;
else
goto set_zero;
}
MPFR_SAVE_EXPO_MARK (expo);
/* Set up initial prec */
prec = MPFR_PREC (dest) + 3 + MPFR_INT_CEIL_LOG2 (MPFR_PREC (dest));
mpfr_init2 (tmp, prec);
MPFR_ZIV_INIT (loop, prec);
if (MPFR_IS_POS (x))
/* use atan2(y,x) = atan(y/x) */
for (;;)
{
mpfr_div (tmp, y, x, GMP_RNDN); /* Error <= ulp (tmp) */
mpfr_atan (tmp, tmp, GMP_RNDN); /* Error <= 2*ulp (tmp) since
abs(D(arctan)) <= 1 */
/*FIXME: Error <= ulp(tmp) ? */
if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp, prec - 2, MPFR_PREC (dest),
rnd_mode)))
break;
MPFR_ZIV_NEXT (loop, prec);
mpfr_set_prec (tmp, prec);
}
else /* x < 0 */
/* Use sign(y)*(PI - atan (|y/x|)) */
{
mpfr_init2 (pi, prec);
for (;;)
{
mpfr_div (tmp, y, x, GMP_RNDN); /* Error <= ulp (tmp) */
MPFR_SET_POS (tmp); /* no error */
mpfr_atan (tmp, tmp, GMP_RNDN); /* Error <= 2*ulp (tmp) since
abs(D(arctan)) <= 1 */
mpfr_const_pi (pi, GMP_RNDN); /* Error <= ulp(pi) /2 */
e = MPFR_GET_EXP (tmp);
mpfr_sub (tmp, pi, tmp, GMP_RNDN); /* see above */
if (MPFR_IS_NEG (y))
MPFR_CHANGE_SIGN (tmp);
/* Error(tmp) <= (1/2+2^(EXP(pi)-EXP(tmp)-1)+2^(e-EXP(tmp)+1))*ulp
<= 2^(MAX (MAX (EXP(PI)-EXP(tmp)-1, e-EXP(tmp)+1),
-1)+2)*ulp(tmp) */
e = MAX (MAX (MPFR_GET_EXP (pi)-MPFR_GET_EXP (tmp) - 1,
e - MPFR_GET_EXP (tmp) + 1), -1) + 2;
if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp, prec - e, MPFR_PREC (dest),
rnd_mode)))
break;
MPFR_ZIV_NEXT (loop, prec);
mpfr_set_prec (tmp, prec);
mpfr_set_prec (pi, prec);
}
mpfr_clear (pi);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (dest, tmp, rnd_mode);
mpfr_clear (tmp);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (dest, inexact, rnd_mode);
}
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